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Numerical methods for biological flows laden with deformable capsules and solid particles Huet, Damien P.


Biological fluids such as blood accomplish many vital tasks in the human body, including carrying oxygen and nutrients to tissues, regulating internal temperature and pH, or transporting white blood cells to infected areas. A better understanding of these fluids can provide insight into many pathologies such as the formation of aneurysms and the effect of sickle cell disease on the flow of red blood cells, as well as help design efficient diagnosis tools on microfluidic devices. Such fluids are composed of a continuous viscous phase and suspended bodies, including rigid particles and deformable membranes enclosing an inner fluid, referred to as capsules. In this thesis, we develop numerical tools aiming to simulate cell-resolved biological fluids such as blood. In a first part, we focus on the dispersed solid phase, a field known as granular mechanics. In this context, we implement a contact force able to accurately model static assemblies of granular media. After extensive validation, we use this contact model in a purely granular setting to study avalanches of entangled particles. Our numerical results are compared to experiments and show very good qualitative and quantitative agreement. Moreover, we present a variety of novel avalanching behaviors, as well as an intermittent regime in which reproducibility is lost. After analyzing the microstructure of granular assemblies in this regime, we conclude that it likely arises from mesoscale clusters of particles. In a second part, we concentrate on flowing biological capsules. We develop an adaptive front-tracking method which enables simulations of capsules in very large geometries for a wide range of Reynolds number. We validate our solver extensively and we show excellent qualitative and quantitative agreement with the literature. We then study the dynamics of capsules flowing through a sharp corner, a commonly encountered geometry in microfluidic devices. We analyze the trajectory, normalized velocity and area variations of the capsules and we show that in our case of strong confinement, the capsules interact weakly unless they are located very close to each other. Finally, we present and implement a fully Eulerian alternative method to simulate flowing capsules, and we highlight its advantages and limits.

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